Transcript 2-Solving Multi-Step Equations

7-2 Solving Multi-Step Equations
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
7-2 Solving Multi-Step Equations
Warm Up
Solve.
1. 3x = 102
x = 34
2. y = 15 y = 225
15
3. z – 100 = 21 z = 121
4. 1.1 + 5w = 98.6 w = 19.5
7-2 Solving Multi-Step Equations
Problem of the Day
Ana has twice as much money as Ben,
and Ben has three times as much as
Clio. Together they have $160. How
much does each person have?
Ana, $96; Ben, $48; Clio, $16
7-2 Solving Multi-Step Equations
Learn to solve multi-step equations.
7-2 Solving Multi-Step Equations
To solve a multi-step equation, you
may have to simplify the equation first
by combining like terms or by using the
Distributive Property.
7-2 Solving Multi-Step Equations
Additional Example 1A: Solving Equations That
Contain Like Terms
Solve.
8x + 6 + 3x – 2 = 37
11x + 4 = 37
–4 –4
11x
= 33
11x = 33
11 11
x=3
Combine like terms.
Subtract 4 from both sides.
Divide both sides by 11.
7-2 Solving Multi-Step Equations
Additional Example 1A Continued
Check
8x + 6 + 3x – 2 = 37
?
8(3) + 6 + 3(3) – 2 = 37
Substitute 3 for x.
?
24 + 6 + 9 – 2 = 37
?
37 = 37 
7-2 Solving Multi-Step Equations
Additional Example 1B: Solving Equations That
Contain Like Terms
Solve.
4(x – 6) + 7 = 11
4(x – 6) + 7 = 11 Distributive Property
4(x) – 4(6) + 7 = 11
Simplify by multiplying:
4x – 24 + 7 = 11 4(x) = 4x and 4(6) = 24.
4x – 17 = 11 Simplify by adding: –24 + 7 = 17.
+ 17 +17 Add 17 to both sides.
4x = 28
4
4 Divide both sides by 4.
x=7
7-2 Solving Multi-Step Equations
Check It Out: Example 1
Solve.
9x + 5 + 4x – 2 = 42
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract 3 from both sides.
13x
= 39
13x = 39 Divide both sides by 13.
13 13
x=3
7-2 Solving Multi-Step Equations
Check It Out: Example 1 Continued
Check
9x + 5 + 4x – 2 = 42
?
9(3) + 5 + 4(3) – 2 = 42
Substitute 3 for x.
?
27 + 5 + 12 – 2 = 42
?
42 = 42 
7-2 Solving Multi-Step Equations
If an equation contains fractions, it may
help to multiply both sides of the
equation by the least common
denominator (LCD) of the fractions. This
step results in an equation without
fractions, which may be easier to solve.
7-2 Solving Multi-Step Equations
Remember!
The least common denominator (LCD) is the
smallest number that each of the denominators
will divide into.
7-2 Solving Multi-Step Equations
Additional Example 2: Solving Equations That
Contain Fractions
Solve.
7x + x – 17 = 2
3
2
9
9
The LCD is 18.
Multiply both
17
7x
x
2
18
+ – 9 = 18
sides by 18.
9
2
3
7x
x
17
2 Distributive
18 9 + 18 2 – 18 9 = 18 3 Property.
()
(
()
)
()
()
()
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
7-2 Solving Multi-Step Equations
Additional Example 2 Continued
23x – 34 = 12
Combine like terms.
+ 34 + 34
23x
= 46
23x = 46
23 23
Add 34 to both sides.
x=2
Divide both sides by 23.
7-2 Solving Multi-Step Equations
Additional Example 2 Continued
Check
7x + x – 17 = 2
2
3
9
9
? 2
7(2) + (2) – 17 =
Substitute 2 for x.
9
2
9
3
14 2 17 ? 2
9 +2 – 9 =3
? 2
14 + 1 – 17 =
9
9
3
14 9 17 ? 6
The LCD is 9.
9 +9 – 9 =9
? 6
6=
9 9
7-2 Solving Multi-Step Equations
Check It Out: Example 2A
Solve.
3n+ 5= – 1
4
4
4
Multiply both sides by 4 to clear fractions,
and then solve.
4 3n + 5 = 4 –1
4
4
4
(
) ( )
5 = 4 –1
4(3n
+
4
(4 ) (4)
4)
3n + 5 = –1
Distributive Property.
7-2 Solving Multi-Step Equations
Check It Out: Example 2A Continued
3n + 5 = –1
– 5 –5
3n
= –6
3n= –6
3
3
n = –2
Subtract 5 from both sides.
Divide both sides by 3.
7-2 Solving Multi-Step Equations
Check It Out: Example 2B
Solve.
5x + x – 13 = 1
3
9
9
3
The LCD is 9.
9 5x + x –
9
3
5x
x
9 9 +9 3 –9
(
) ()
() () () ()
13 = 9 1
3
9
13
1
9 =9 3
Multiply both
sides by 9.
Distributive
Property.
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.
7-2 Solving Multi-Step Equations
Check It Out: Example 2B Continued
8x – 13 = 3
Combine like terms.
+ 13 + 13
8x
= 16
8x = 16
8
8
Add 13 to both sides.
x=2
Divide both sides by 8.
7-2 Solving Multi-Step Equations
Check It Out: Example 2B Continued
Check
5x + x – 13 = 1
3
3
9
9
? 1
5(2) + (2) – 13 =
Substitute 2 for x.
9
3
9
3
10 2 13 ? 1
9 +3 – 9 =3
? 3
10 + 6 – 13 =
The LCD is 9.
9
9
9
9
? 3
3=
9 9
7-2 Solving Multi-Step Equations
Additional Example 3: Travel Application
On Monday, David rides his bicycle m miles in
2 hours. On Tuesday, he rides three times as
far in 5 hours. If his average speed for the two
days is 12 mi/h, how far did he ride on
Monday? Round your answer to the nearest
tenth of a mile.
David’s average speed is his total distance for the
two days divided by the total time.
Total distance
Total time
= average speed
7-2 Solving Multi-Step Equations
Additional Example 3 Continued
m + 3m
= 12
2+5
4m
= 12
7
Substitute m + 3m for total
distance and 2 + 5 for total time.
Simplify.
7 4m = 7(12) Multiply both sides by 7.
7
4m = 84
4m = 84
Divide both sides by 4.
4
4
m = 21
David rode 21.0 miles.
7-2 Solving Multi-Step Equations
Check It Out! Example 3
On Saturday, Penelope rode her scooter m
miles in 3 hours. On Sunday, she rides twice
as far in 7 hours. If her average speed for two
days is 20 mi/h, how far did she ride on
Saturday? Round your answer to the nearest
tenth of a mile.
Penelope’s average speed is her total distance for
the two days divided by the total time.
Total distance
Total time
= average speed
7-2 Solving Multi-Step Equations
Check It Out! Example 3 Continued
m + 2m
= 20
3+7
3m
= 20
10
Substitute m + 2m for total
distance and 3 + 7 for total time.
Simplify.
10 3m = 10(20) Multiply both sides by 10.
10
3m = 200
3m = 200 Divide both sides by 3.
3
3
m  66.67
Penelope rode approximately 66.7 miles.
7-2 Solving Multi-Step Equations
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
7-2 Solving Multi-Step Equations
Lesson Quiz
Solve.
1. 6x + 3x – x + 9 = 33 x = 3
2. 8(x + 2) + 5 = 29
3. 5 + x = 33
8
8
8
4. 6x – 2x = 25
21
7
21
x=1
x = 28
9
x = 116
5. Linda is paid double her normal hourly rate for each
hour she works over 40 hours in a week. Last week
she worked 52 hours and earned $544. What is her
hourly rate? $8.50
7-2 Solving Multi-Step Equations
Lesson Quiz for Student Response Systems
1. Solve 4p + 13 + 11p = 88
A. p = 5
B. p = 7
C. p = 75
D. p = 91
7-2 Solving Multi-Step Equations
Lesson Quiz for Student Response Systems
2. Solve 4(x + 3) + 5 = 109
A. x = 4
B. x = 23
C. x = 26
D. x = 101
7-2 Solving Multi-Step Equations
Lesson Quiz for Student Response Systems
3. Solve
A. x = 5
B. x = 6
C. x = 21
D. x = 101
.